A library of operators
Principles
We consider the Leaky Integrate-and-Fire (LIF) model, where spiking neurons can be considered as leaky integrators across time and space of the weighted outputs of other neurons. A neuron emits an output spikes and resets its potential when reaching its threshold. Signals are encoded using the instantaneous firing rate of neurons.
The behavior of a group of neurons is determined by the neurons' parameters connections neurons. For example, an addition of two signals can easily be implented with one neuron with two inputs: synaptic weights are set to the neuron threshold, meaning each input spike induces an output spike. Output firing frequency is thus the sum of the two input frequencies.
Performing an addition of two signals with one neuron.
The combination of spike-rate coding with analog neurons results in a computing scheme that is extremely robust to hardware variability and defects, while being energy-efficient for certain classes of applications.
Library
A given group of spiking neurons can implement a broad set of operators, and particularly operators well suited for signal-processing tasks. We are developing a library of operators, including:
- adder
- subtractor
- multiplier
- spatial derivation
- temporal derivation
- temporal integration
- maximum, minimum
- multiplexer (logical IF)
- logical AND
- convolution, correlation
- oscillators, clocks
- ...
Composition of operators
Elementary operators can be composed to build higher-level functions and applications. The result of such a composition of operators can be seen as directed graph (nodes represent neurons, edges are synaptic connections) that has to be mapped on the physical architecture.
Connectivity graph of a 20 samples-long correlation.
